Largest well-posed spaces for the general diffusion system with nonlocal interactions

The authors derive a general diffusion (GD) system with nonlocal interactions of special structure via energetic variational approach and observe that there exist two critical values of s, i.e. s=12,1, for the nonlocal interactions, where s=12 reflects how strong nonlocal property we have and s=1 affects the linearization and choice of initial data spaces. The authors also establish the global existence and uniqueness of mild solution.